4 Answers
4

You can find sine of angle $B$ using sine rule: $sin\beta=(2.71\cdot sin46)/2.29=0.85 \Rightarrow \beta=58.35$. You got this correctly. Now, using the fact that sum of angles in triangle is 180 degrees, you get angle $C=180-46-58.35=75.65$ (all angles are in degrees).

Once you have two angles, there's no need to re-use sine rule. Calculation is more complicated and you can make a mistake more easily.

While the other answers have covered the basic use of the Law of Sines, they've all missed a critical point: there are two triangles that fit your given information. Here is the triangle you've found:

But, when you're solve $\sin B=\frac{b\sin A}{a}$, there are two solutions that could be angles in a triangle, $B_1=\arcsin\left(\frac{b\sin A}{a}\right)$ (the one you found) and $B_2=180°-\arcsin\left(\frac{b\sin A}{a}\right)$. Using this second possible measure for $B$ won't always yield a triangle, but in this case it does: